A numerical method for determining monotonicity and convergence rate in iterative learning control

An iterative learning control algorithm with an adjustable interval is proposed for nonlinear systems to accelerate the convergence rate of iterative learning control. Forλ-norm, the monotonic convergence of ILC was analyzed, and the corresponding convergence conditions were obtained. The results showed that the convergence rate was mainly determined by the controlled object, the control law gain, the correction factor, and the iteration interval size and that the control law gain was corrected in real time in the modified interval and the modified interval shortened as the number of iterations increased, further accelerating the convergence. The numerical simulation shows the effectiveness of the proposed method.

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Frequency Dependent Nonlinear Iterative Learning Control With Application to a Wafer Stage

Volume 4A: Dynamics, Vibration and Control ◽

10.1115/imece2013-62054 ◽

2013 ◽

Author(s):

Dongdong Yu ◽

Yu Zhu ◽

Kaiming Yang ◽

Xin Li ◽

Yi Jiang

Keyword(s):

Convergence Rate ◽

Iterative Learning Control ◽

Learning Control ◽

Iterative Learning ◽

Planar Motion ◽

Learning Gain ◽

Motion Stage ◽

Long Stroke ◽

Noise Amplification ◽

Planar Motion Stage

This paper deals with the control design of a wafer stage setup, catering for the increasing demand for ultra-precision positioning and high throughput devices in line with further miniaturization of the LCD, semiconductor and electronic parts. The developed wafer stage employs a dual stroke principle: a short stroke for fine positioning and a long stroke for coarse positioning. The short stroke is a stage of six-degree-of-freedom with integrated magnetic bearing to counteract the gravity, while the long stroke is a planar motion stage consisting of a integrated three-axis drive motor, which can move along the surface of the Halbach permanent magnet array without generating friction due to being elevated with air bearings. To achieve precision tracking control with zero settling time under high acceleration/velocity motion, iterative learning control has been regarded as an effective means. Linear iterative learning control techniques attenuate the recurring disturbances and amplify the nonrecurring, suffering from a fixed trade-off between convergence rate and noise amplification. In this paper, a frequency dependent amplitude-based nonlinear iterative learning control is proposed. Within a frequency range of interest, the learning gain is continuously updated to improve the control performance of the planar motion stage. Based on the frequency contents of error signal, for error-levels beyond a predefined threshold, additional learning gain will be effectively used to diminish the low-frequency tracking error. Below the threshold, the original low-gain value is maintained to avoid high-frequency noise amplification. Performance assessment on the developed wafer stage setup shows that the proposed nonlinear iterative learning strategy can realize a remarkable performance which includes nanometer positioning and tracking over large travel ranges, and provides a more desirable means to deal with the convergence rate and noise amplification.

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An Improved Method for Calculating Iterative Learning Control Convergence Rate

ASME 2008 Dynamic Systems and Control Conference, Parts A and B ◽

10.1115/dscc2008-2180 ◽

2008 ◽

Author(s):

Kira Barton ◽

Andrew Alleyne ◽

Doug Bristow

Keyword(s):

Convergence Rate ◽

Iterative Learning Control ◽

Learning Algorithm ◽

Linear Time ◽

Learning Control ◽

Iterative Learning ◽

Arnoldi Method ◽

Dynamic Simulations ◽

Large Matrix ◽

Implicitly Restarted Arnoldi

In Iterative Learning Control (ILC), the lifted system is often used in design and analysis to determine convergence rate of the learning algorithm. Computation of the convergence rate in the lifted setting requires construction of large NxN matrices, where N is the number of data points in an iteration. The convergence rate computation is O(N2) and is typically limited to short iteration lengths because of computational memory constraints. In this article, we present an alternative method for calculating the convergence rate without the need of large matrix calculations. This method uses the implicitly restarted Arnoldi method and dynamic simulations to calculate the ILC norm, reducing the calculation to O(N). In addition to faster computation, we are able to calculate the convergence rate for long iteration lengths. This method is presented for multi-input multi-output, linear time-varying discrete-time systems.

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